Let the common axis be the z-axis.
C1 is at z=−d, C2 is at z=0, and C3 is at z=+d.
Current in C1 is anti-clockwise (ACW), producing a magnetic field B1 in the +z direction at C2.
Current in C3 is clockwise (CW), producing a magnetic field B3 in the −z direction at C2.
The net magnetic field at C2 is Bnet=B1−B3. Since C1 and C3 are equidistant and carry equal current, initially Bnet=0.
To induce a clockwise current in C2, Lenz's law states that the induced current must oppose the change in flux. A clockwise induced current produces a magnetic field in the −z direction.
This happens if there is an increasing flux in the +z direction or a decreasing flux in the −z direction.
Case 1: C1 moves towards C2. The distance decreases, so B1 (in +z direction) increases. This causes an increasing flux in the +z direction.
Case 2: C3 moves away from C2. The distance increases, so B3 (in −z direction) decreases. This causes a decreasing flux in the −z direction.
Both actions (moving C1 towards C2 and moving C3 away from C2) result in a net change in flux that induces a clockwise current in C2 to oppose the change.
Therefore, option (3) is correct.